A new discontinuous Galerkin method for Kirchhoff plates

A general framework of constructing C 0 discontinuous Galerkin (CDG) methods is developed for solving the Kirchhoff plate bending problem, following some ideas in (Castillo et al., 2000) [10] and (Cockburn, 2003) [12]. The numerical traces are determined based on a discrete stability identity, which lead to a class of stable CDG methods. A stable CDG method, called the LCDG method, is particularly interesting in our study. It can be viewed as an extension to fourth-order problems of the LDG method studied in (Castillo et al., 2000) [10] and (Cockburn, 2003) [12]. For this method, optimal order error estimates in certain broken energy norm and H 1 -norm are established. Some numerical results are reported, confirming the theoretical convergence orders.